# Conjugacy Class 1 of Group S4Z2

Cable 1:[3, 1, 4, 2, 6, 5].
Disjoint cycle form: [[1, 3, 4, 2], [5, 6]].
Cable 2:[1, 2, 4, 3, 5, 6].
Disjoint cycle form: [[3, 4]].
• Example 1_1
```CC2_CLASS = 1, example 1:
Strut: [2, 1, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[1, 2], [3, 4]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .292893 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3br]

```
```
VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

```
• Example 1_2
```CC2_CLASS = 1, example 2:
Strut: [1, 4, 3, 2, 6, 5]. 	 Disjoint cycle form:  [[2, 4], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .285714 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_3
```CC2_CLASS = 1, example 3:
Strut: [4, 2, 1, 3, 5, 6]. 	 Disjoint cycle form:  [[1, 4, 3]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .118082 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_4
```CC2_CLASS = 1, example 4:
Strut: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .310102 occurring in representation dim3br.

```
```

```
• Example 1_5
```CC2_CLASS = 1, example 5:
Strut: [3, 4, 1, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3], [2, 4], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_6
```CC2_CLASS = 1, example 6:
Strut: [1, 2, 4, 3, 6, 5]. 	 Disjoint cycle form:  [[3, 4], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .2 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_7
```CC2_CLASS = 1, example 7:
Strut: [3, 4, 1, 2, 5, 6]. 	 Disjoint cycle form:  [[1, 3], [2, 4]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .333333 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3br]

```
```
VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

```
• Example 1_8
```CC2_CLASS = 1, example 8:
Strut: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .2 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_9
```CC2_CLASS = 1, example 9:
Strut: [1, 3, 2, 4, 5, 6]. 	 Disjoint cycle form:  [[2, 3]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .181818 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_10
```CC2_CLASS = 1, example 10:
Strut: [3, 1, 2, 4, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 2], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .354248 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_11
```CC2_CLASS = 1, example 11:
Strut: [4, 1, 2, 3, 6, 5]. 	 Disjoint cycle form:  [[1, 4, 3, 2], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .142857 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_12
```CC2_CLASS = 1, example 12:
Strut: [3, 2, 4, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .198062 occurring in representation dim3br.

```
```

```
• Example 1_13
```CC2_CLASS = 1, example 13:
Strut: [4, 3, 2, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 4], [2, 3]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is 1 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3b, dim3br]

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.
DEGENERATE EDGES: 1 edge(s) of length 0.

```
• Example 1_14
```CC2_CLASS = 1, example 14:
Strut: [3, 1, 2, 4, 5, 6]. 	 Disjoint cycle form:  [[1, 3, 2]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .118082 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_15
```CC2_CLASS = 1, example 15:
Strut: [2, 4, 1, 3, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 4, 3]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .090909 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_16
```CC2_CLASS = 1, example 16:
Strut: [2, 1, 3, 4, 5, 6]. 	 Disjoint cycle form:  [[1, 2]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .333333 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3br]

```
```
VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

```
• Example 1_17
```CC2_CLASS = 1, example 17:
Strut: [3, 2, 1, 4, 5, 6]. 	 Disjoint cycle form:  [[1, 3]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .4 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_18
```CC2_CLASS = 1, example 18:
Strut: [4, 3, 2, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [2, 3], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_19
```CC2_CLASS = 1, example 19:
Strut: [4, 3, 1, 2, 5, 6]. 	 Disjoint cycle form:  [[1, 4, 2, 3]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .292893 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3br]

```
```
VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

```
• Example 1_20
```CC2_CLASS = 1, example 20:
Strut: [2, 1, 3, 4, 6, 5]. 	 Disjoint cycle form:  [[1, 2], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .2 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_21
```CC2_CLASS = 1, example 21:
Strut: [1, 2, 3, 4, 6, 5]. 	 Disjoint cycle form:  [[5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_22
```CC2_CLASS = 1, example 22:
Strut: [4, 3, 1, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 4, 2, 3], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .1 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```
• Example 1_23
```CC2_CLASS = 1, example 23:
Strut: [2, 1, 4, 3, 6, 5]. 	 Disjoint cycle form:  [[1, 2], [3, 4], [5, 6]].
Cable 1: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 2: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

```
```
VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

```